where \(D\)  is the deformation potential, \(\rho _m=7.6\times 10^{-8}\)  g/cm\(^2\)  is the graphene mass density, \(v_{ph}=2\times 10^4\)  m/s is the LA phonon velocity [1]} and \(v_F=1\times 10^6\)  m/s is the Fermi velocity [2]}. While our data in Fig. 3 show clearly such a linear \(T\) -dependence, indicative of phonon scattering, the slope of \(\rho (T)\)  displays an unexpected density dependence, not captured by Eq. (1). The origin of this density dependence is unclear. It may point to additional contributions from a different \(T\) -dependent scattering mechanisms at lower densities, such as screened Coulomb scattering [3]}. Further experimental and theoretical work is needed to resolve this issue. However, for large \(|n|\) , when \(\Delta \rho /\Delta T(n)\)  in Fig. 3b reaches a roughly \(n\) -independent value (at least for positive \(V_g\) ) we may identify this limiting behavior with exclusively phonon scattering and derive an upper bound value for \(D\) . For \(n=+2\times 10^{11}\)  cm\(^{-2}\)  (electrons) Eq. (1) yields \(D \sim \)  29 eV, consistent with \(D=10-30\)  eV in graphite [4]}, [1]} and comparable to \(D\sim 17\)  eV, reported for unsuspended graphene [6]}. In contrast, for \(n=-2\times 10^{11}\)  cm\(^{-2}\)  (holes) we obtain \(D\sim 50\)  eV. This value may be overestimated, since \(\Delta \rho /\Delta T (n)\)  is not fully saturated even at \(V_g \approx \) -5 V, the experimental limit of hole density. Nevertheless, this large asymmetry is unusual and presently unresolved and, together with the observed \(n\)  dependence, may point to a scattering behavior in suspended graphene that is more complex than simple electron-phonon interaction.
